Odds on Flopping Trips or Two Pair in Hold'em

[theBruiser500]

If you have two cards which are not paired, what are the odds that you will flop trips? What are the odds you will flop two pair?

danny

[bigpooch]

There are C(50,3) = 19600 possible flops of which the
following give the distribution of hands (for a nonpaired
starting hand in HE):

quads: 1
full house: 2x3x3 = 18
trips only: 2x3x11x4 = 264
two pairs: 3x3x11x4 = 396

total: 880

The chances of two pairs or better are then 880/19600 or
about 0.044898 or about 4.5%.

[Analyst]

[ QUOTE ]
There are C(50,3) = 19600 possible flops of which the
following give the distribution of hands (for a nonpaired
starting hand in HE):

quads: 1
full house: 2x3x3 = 18
trips only: 2x3x11x4 = 264
two pairs: 3x3x11x4 = 396

total: 880

The chances of two pairs or better are then 880/19600 or
about 0.044898 or about 4.5%.

[/ QUOTE ]

Ummm . . . just to nit-pick, there are 2 flops which will give quads, not 1. Not that this changes the probability of overall improvement by much, though. /images/graemlins/wink.gif

On the not-nit-picky side, the total doesn't come out to 880, but rather 680, making the odds of improvement about 3.5%, not 4.5%.

Also, the odds of someone flopping a full house when I have a good hand seem to be much higher than the figures above!

[BradleyT]

What are the odds that Ace-trash will call my all in and beat my QQ or KK?

Seems to be 100% lately.

[ajizzle]

There are 50c3 possible flops, and 48*6c2 will give you trips or two pair, 6c3 will give you quads or full house.

So (48*6c2+6c3)/(50c3)

Hope that helps

[bigpooch]

Correct that there are 2 flops for quads but it must clearly
be a typo (the sum for hands of two pairs or better is also
a typo!). Also, the sum is incorrect and is not 880 but is
680 (I wasn't drunk though!). The correct numbers should
be:

quads: 2
full house: 18
trips: 264
two pairs: 396

total: 680

and the percentage is then 3.469%.

[BradleyT]

What branch of math other than "statistics" should a person study to learn how to calculate these numbers and percentages?

[ajizzle]

Logic. Probability (not statistics) will help you figure your odds when playing against any random hand. Logic, specifically poker logic, will help you narrow down the hands your opponent could hold, and then add probabilities to them holding those hands. At that point, you can then use probability to figure out the chances that you can beat those hands.

Ajizzle

[Stephen Keller]

[ QUOTE ]
48*6c2 will give you trips or two pair, 6c3 will give you quads or full house.


[/ QUOTE ]

Would you mind explaining how you come to the formula for calculating those? I get 50c3 for the flops, but not the other two.

Thanks.

[bigpooch]

Not quite. There are 44 x C(6,2) trips or two pairs and
C(6,3) full houses or better; these numbers are 660 and 20
respectively. Apparently, you just forgot to remove another
rank from the deck of 52 cards.